# Branch locus of a projection

I'm looking for a formula or quick trick for computing the branch locus of a hypersurface under projection. My specific case:

Let $V\subset\mathbb{P}^3$ be a surface of degree $d$, $p\in\mathbb{P}^3$ (it's actually a node of $V$, if that's relevant), and I'm attempting to compute the branch locus of the projection $V\dashrightarrow \mathbb{P}^2$, which should be a plane curve.

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